Mathematics · Geometry

Trapezoid Area Calculator

Find trapezoid area from the two parallel base lengths and perpendicular height.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Live constructionTrapezoid
TrapezoidA trapezoid with parallel bases 6 and 10 and height 4.a = 6b = 10h = 4

Change an input to reshape this diagram.

Your inputCalculatedPassed forward in chains
Area32
Average base8

Calculation steps

  1. Add bases: 6 + 10 = 16.
  2. Average base = 16 ÷ 2 = 8.
  3. Area = 8 × 4 = 32.

Understand Trapezoid area

One idea, three depths

Choose how deeply to explain Trapezoid area

Find trapezoid area from the two parallel base lengths and perpendicular height.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Trapezoid area to answer this question: find trapezoid area from the two parallel base lengths and perpendicular height? Enter First base, Second base, Perpendicular height; the calculator shows Area. For example: Bases 6 and 10 with height 4 give (6 + 10) × 4 ÷ 2 = 32 square units. The answer tells you Area.

Age 15Explain it to a 15-year-oldConnect it to the formula

The area equals the average length of the parallel sides multiplied by their perpendicular separation. The rule is A = (a + b)h ÷ 2. Its input values are First base, Second base, Perpendicular height, and the main result is Area. For example: Bases 6 and 10 with height 4 give (6 + 10) × 4 ÷ 2 = 32 square units.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated trapezoid area relation over the valid real-number domain stated below. The implemented relation is A = (a + b)h ÷ 2, evaluated from First base, Second base, Perpendicular height to produce Area. The area equals the average length of the parallel sides multiplied by their perpendicular separation. Use the perpendicular height, not the length of a slanted side.

Inputs and valid domain

  • First base must be a finite real number, at least 0.
  • Second base must be a finite real number, at least 0.
  • Perpendicular height must be a finite real number, at least 0.

Important boundary: Use the perpendicular height, not the length of a slanted side.

The formula

A = (a + b)h ÷ 2

How the calculator works through it

It substitutes First base, Second base, Perpendicular height into the formula and exposes every numerical step above. The main output is Area, accompanied by Average base.

Read the result correctly

The Area is the direct answer to “find trapezoid area from the two parallel base lengths and perpendicular height.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

Bases 6 and 10 with height 4 give (6 + 10) × 4 ÷ 2 = 32 square units.

Where this model stops being reliable

Use the perpendicular height, not the length of a slanted side.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Trapezoid area works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Trapezoid area uses A = (a + b)h ÷ 2. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

Optional enrichment

  • Angles and geometric relationships

    Angle language provides useful geometric context for extending Trapezoid area to related shapes and constructions.

    Review this foundation about 4 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read First base, Second base, Perpendicular height.
  2. Evaluate the principal relationship: A = (a + b)h ÷ 2.
  3. Return Area and check the domain conditions described above.
Python
            from math import *

def trapezoid_area(a, b, height) -> float:
    return (((a + b) * height) / 2.0)

assert abs(trapezoid_area(6, 10, 4) - 32) < 1e-6 * max(1.0, abs(32))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double trapezoid_area(double a, double b, double height) {
    return (((a + b) * height) / 2.0);
}

int main(void) {
    const double expected = 32;
    const double actual = trapezoid_area(6, 10, 4);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double trapezoid_area(double a, double b, double height) {
    return (((a + b) * height) / 2.0);
}

int main() {
    constexpr double expected = 32;
    const double actual = trapezoid_area(6, 10, 4);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double trapezoid_area(double a, double b, double height)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global trapezoid_area
section .text

trapezoid_area:
    push rbp
    mov rbp, rsp
    sub rsp, 64
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd [rbp-24], xmm2
    movsd xmm0, [rbp-8]
    addsd xmm0, [rbp-16]
    movsd [rbp-48], xmm0
    movsd xmm0, [rbp-48]
    mulsd xmm0, [rbp-24]
    movsd [rbp-40], xmm0
    mov rax, 0x4000000000000000
    movq xmm0, rax
    movsd [rbp-56], xmm0
    movsd xmm0, [rbp-40]
    divsd xmm0, [rbp-56]
    movsd [rbp-32], xmm0
    movsd xmm0, [rbp-32]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = trapezoid_area(a, b, height)
    result = (((a + b) * height) / 2.0);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[a_, b_, height_] := (((a + b) * height) / 2.0);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Algebra and Trigonometry 2e

Read the related free OpenStax mathematics chapters
Cite this book
APA 7
Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
MLA 9
Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
Chicago author-date
Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Trapezoid Area Calculator. MW SysArc Tools. https://math.mwsysarc.com/geometry/trapezoid-area-calculator

MLA 9

MW SysArc. “Trapezoid Area Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/trapezoid-area-calculator. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Trapezoid Area Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/trapezoid-area-calculator.

Harvard

MW SysArc (2026) ‘Trapezoid Area Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/trapezoid-area-calculator (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_trapezoid_area_2026,
  author = {{MW SysArc}},
  title = {Trapezoid Area Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/geometry/trapezoid-area-calculator},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Trapezoid Area Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/geometry/trapezoid-area-calculator
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Trapezoid area do?

Find trapezoid area from the two parallel base lengths and perpendicular height.

How does the Trapezoid area work?

The calculator applies A = (a + b)h ÷ 2. The area equals the average length of the parallel sides multiplied by their perpendicular separation.

What can I learn from the Trapezoid area?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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